A baseball player is to play in the World Series. Based upon his season play, you estimate that if he comes to bat four times in a game the number of hits he will get has a distribution
pX=(0.41.22.23.14.1).
Assume that the player comes to bat four times in each game of the series.
(a) Let X denote the number of hits that he gets in a series. Using the program NFoldConvolution, find the distribution of X for each of the possible series lengths: four-game, five-game, six-game, seven-game.
(b) Using one of the distributions found in part (a), find the probability that his batting average exceeds .400 in a four-game series. (The batting average is the number of hits divided by the number of times at bat.)
(c) Given the distribution pX, what is his long-term batting average?